Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across splits already predict much of the generated images. To formalize this, we develop a random matrix theory (RMT) framework that quantifies how finite datasets shape the expectation and variance of the learned denoiser and sampling map in the linear setting. For expectations, sampling variability acts as a renormalization of the noise level through a self-consistent relation $σ^2 \mapsto κ(σ^2)$, explaining why limited data overshrink low-variance directions and pull samples toward the dataset mean. For fluctuations, our variance formulas reveal three key factors behind cross-split disagreement: \textit{anisotropy} across eigenmodes, \textit{inhomogeneity} across inputs, and overall scaling with dataset size. Extending deterministic-equivalence tools to fractional matrix powers further allows us to analyze entire sampling trajectories. The theory sharply predicts the behavior of linear diffusion models, and we validate its predictions on UNet and DiT architectures in their non-memorization regime, identifying where and how samples deviates across training data split. This provides a principled baseline for reproducibility in diffusion training, linking spectral properties of data to the stability of generative outputs.

Objective: Deep learning-based deformable image registration has achieved strong accuracy, but remains sensitive to variations in input image characteristics such as artifacts, field-of-view mismatch, or modality difference. We aim to develop a general training paradigm that improves the robustness and generalizability of registration networks. Methods: We introduce surrogate supervision, which decouples the input domain from the supervision domain by applying estimated spatial transformations to surrogate images. This allows training on heterogeneous inputs while ensuring supervision is computed in domains where similarity is well defined. We evaluate the framework through three representative applications: artifact-robust brain MR registration, mask-agnostic lung CT registration, and multi-modal MR registration. Results: Across tasks, surrogate supervision demonstrated strong resilience to input variations including inhomogeneity field, inconsistent field-of-view, and modality differences, while maintaining high performance on well-curated data. Conclusions: Surrogate supervision provides a principled framework for training robust and generalizable deep learning-based registration models without increasing complexity. Significance: Surrogate supervision offers a practical pathway to more robust and generalizable medical image registration, enabling broader applicability in diverse biomedical imaging scenarios.

Magnetic resonance imaging (MRI) has significantly benefited from the resurgence of artificial intelligence (AI). By leveraging AI's capabilities in large-scale optimization and pattern recognition, innovative methods are transforming the MRI acquisition workflow, including planning, sequence design, and correction of acquisition artifacts. These emerging algorithms demonstrate substantial potential in enhancing the efficiency and throughput of acquisition steps.

Identifying constitutive parameters in engineering and biological materials, particularly those with intricate geometries and mechanical behaviors, remains a longstanding challenge. The recent advent of Physics-Informed Neural Networks (PINNs) offers promising solutions, but current frameworks are often limited to basic constitutive laws and encounter practical constraints when combined with experimental data. In this paper, we introduce a robust PINN-based framework designed to identify material parameters for soft materials, specifically those exhibiting complex constitutive behaviors, under large deformation in plane stress conditions. Distinctively, our model emphasizes training PINNs with multi-modal synthetic experimental datasets consisting of full-field deformation and loading history, ensuring algorithm robustness even with noisy data. Our results reveal that the PINNs framework can accurately identify constitutive parameters of the incompressible Arruda-Boyce model for samples with intricate geometries, maintaining an error below 5%, even with an experimental noise level of 5%. We believe our framework provides a robust modulus identification approach for complex solids, especially for those with geometrical and constitutive complexity.

$B_1^+$ and $B_0$ field-inhomogeneities can significantly reduce accuracy and robustness of MRF's quantitative parameter estimates. Additional $B_1^+$ and $B_0$ calibration scans can mitigate this but add scan time and cannot be applied retrospectively to previously collected data. Here, we proposed a calibration-free sequence-adaptive deep-learning framework, to estimate and correct for $B_1^+$ and $B_0$ effects of any MRF sequence. We demonstrate its capability on arbitrary MRF sequences at 3T, where no training data were previously obtained. Such approach can be applied to any previously-acquired and future MRF-scans. The flexibility in directly applying this framework to other quantitative sequences is also highlighted.

Brain segmentation from neonatal MRI images is a very challenging task due to large changes in the shape of cerebral structures and variations in signal intensities reflecting the gestational process. In this context, there is a clear need for segmentation techniques that are robust to variations in image contrast and to the spatial configuration of anatomical structures. In this work, we evaluate the potential of synthetic learning, a contrast-independent model trained using synthetic images generated from the ground truth labels of very few subjects.We base our experiments on the dataset released by the developmental Human Connectome Project, for which high-quality T1- and T2-weighted images are available for more than 700 babies aged between 26 and 45 weeks post-conception. First, we confirm the impressive performance of a standard Unet trained on a few T2-weighted volumes, but also confirm that such models learn intensity-related features specific to the training domain. We then evaluate the synthetic learning approach and confirm its robustness to variations in image contrast by reporting the capacity of such a model to segment both T1- and T2-weighted images from the same individuals. However, we observe a clear influence of the age of the baby on the predictions. We improve the performance of this model by enriching the synthetic training set with realistic motion artifacts and over-segmentation of the white matter. Based on extensive visual assessment, we argue that the better performance of the model trained on real T2w data may be due to systematic errors in the ground truth. We propose an original experiment combining two definitions of the ground truth allowing us to show that learning from real data will reproduce any systematic bias from the training set, while synthetic models can avoid this limitation. Overall, our experiments confirm that synthetic learning is an effective solution for segmenting neonatal brain MRI. Our adapted synthetic learning approach combines key features that will be instrumental for large multi-site studies and clinical applications.

Quantitative MRI (qMRI) refers to a class of MRI methods for quantifying the spatial distribution of biological tissue parameters. Traditional qMRI methods usually deal separately with artifacts arising from accelerated data acquisition, involuntary physical motion, and magnetic-field inhomogeneities, leading to suboptimal end-to-end performance. This paper presents CoRRECT, a unified deep unfolding (DU) framework for qMRI consisting of a model-based end-to-end neural network, a method for motion-artifact reduction, and a self-supervised learning scheme. The network is trained to produce R2* maps whose k-space data matches the real data by also accounting for motion and field inhomogeneities. When deployed, CoRRECT only uses the k-space data without any pre-computed parameters for motion or inhomogeneity correction. Our results on experimentally collected multi-Gradient-Recalled Echo (mGRE) MRI data show that CoRRECT recovers motion and inhomogeneity artifact-free R2* maps in highly accelerated acquisition settings. This work opens the door to DU methods that can integrate physical measurement models, biophysical signal models, and learned prior models for high-quality qMRI.

Real world data often exhibit inhomogeneity - complexity of the target function, noise level, etc. are not uniform over the input space. We address the issue of estimating locally optimal kernel bandwidth as a way to describe inhomogeneity. Estimated kernel bandwidths can be used not only for improving the regression/classification performance, but also for Bayesian optimization and active learning, i.e., we need more samples in the region where the function complexity and the noise level are higher. Our method, called kernel mixture of kernel experts regression (KMKER) follows the concept of mixture of experts, which is constituted of several complementary inference models, the so called experts, where in advance a latent classifier, called the gate, predicts the best fitting expert for each test input to infer. For the experts we implement Gaussian process regression models at different (global) bandwidths and a multinomial kernel logistic regression model as the gate. The basic idea behind mixture of experts is, that several distinct ground truth functions over a joint input space drive the observations, which one may want to disentangle. Each expert is meant to model one of the incompatible functions such that each expert needs its individual set of hyperparameters. We differ from that idea in the sense that we assume only one ground truth function which however exhibits spacially inhomogeneous behavior. Under these assumptions we share the hyperparameters among the experts keeping their number constant. We compare KMKER to previous methods (which cope with inhomogeneity but do not provide the optimal bandwidth estimator) on artificial and benchmark data and analyze its performance and capability for interpretation on datasets from quantum chemistry. We also demonstrate how KMKER can be applied for automatic adaptive grid selection in fluid dynamics simulations.

Given a set of known numbers, there are many measures of the degree of inhomogeneity within the set such as the standard deviation, the relative mean difference, and the Gini coefficient. This paper discusses conceptual issues (such as qualitative versus quantitative diversity, and the group as a population versus as a sample), desired properties (such as symmetry and invariance properties), and technical considerations (such as working with differences versus deviations, or absolute versus squared values) in choosing an index suitable for describing the degree of inhomogeneity or diversity in a group of people or computer agents. In particular, it is argued that the relative mean difference and the Gini coefficient are not well-suited as indexes of cultural diversity. This paper then addresses two apparently neglected inverse problems: Given a pre-specified degree of inhomogeneity, what set of unknown numbers has the desired degree of inhomogeneity? And, in particular, what set has the maximal possible degree of inhomogeneity? The solution requires that the set of permissible numbers be bounded with minimum and maximum values. A key benefit of such inverse procedures is that agent-based groups with pre-selected degrees of cultural diversity can be formed to test hypotheses using the full range of possible diversities and thereby avoid statistical problems due to restriction of range effects.